Water level involving Density, mass, volume, radius

In summary, the possible effects on the water level L when a new solid sphere is placed in a bowl of water depend on the density and mass of the new sphere compared to the original sphere. If the new sphere has a higher density and a smaller radius, the water level will rise. If the new sphere has a higher mass and the same density, the water level will remain unchanged. If the new sphere has the same density and a smaller mass or radius, the water level will fall. If the new sphere has a lower density and the same mass, the water level will remain unchanged. If the new sphere has the same mass and a higher density, the water level can either fall or remain unchanged.
  • #1
Jessica1234
1
0

Homework Statement


A small solid sphere of mass M0, of radius R0, and of uniform density ρ0 is placed in a large bowl containing water. It floats and the level of the water in the dish is L. Given the information below, determine the possible effects on the water level L, (R-Rises, F-Falls, U-Unchanged), when that sphere is replaced by a new solid sphere of uniform density.

1. The new sphere has density ρ > ρ0 and radius R < R0
2. The new sphere has mass M > M0 and density ρ = ρ0
3. The new sphere has density ρ = ρ0 and mass M < M0
4. The new sphere has radius R = R0 and mass M < M0
5. The new sphere has density ρ < ρ0 and mass M = M0
6. The new sphere has mass M = M0 and density ρ > ρ0

Homework Equations


d=m/v, Fb=pgv

The Attempt at a Solution


1. R or F or U
2. R or U
3. F
4. F
5. U
6. F or Ureally struggling with this problem, have tried multiple attempts, really just want to understand this problem and what I did wrong. Thanks
 
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  • #2
Welcome to PF!

Can you explain your reasoning for #2?
 

1. What is the relationship between water level and density?

The relationship between water level and density is that as the water level increases, the density also increases. This is because the weight of the water above exerts more pressure on the water below, making it more compact and increasing its density.

2. How does mass affect water level?

The mass of an object has a direct impact on the water level. When an object with a greater mass is placed in water, it displaces more water and causes the water level to rise. This is known as the Archimedes' principle.

3. How is volume related to water level?

The volume of a liquid also affects the water level. When a larger volume of liquid is added to a container, the water level rises. This is because the liquid takes up more space and displaces the water in the container.

4. What is the significance of radius in determining water level?

The radius of a container or object plays a role in determining the water level. A larger radius means there is more space for the water to spread out, resulting in a higher water level. Conversely, a smaller radius means less space for the water to occupy, resulting in a lower water level.

5. How does the shape of a container affect water level?

The shape of a container can also impact the water level. For example, a container with a wider base will have a higher water level compared to a container with a narrower base, even if they have the same volume. This is because the wider base provides more space for the water to spread out and occupy.

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